1. Take flight from your home destination to Skiathos airport
Tipp: Its cheap when you book early!
Airlines from Germany:
From Düsseldorf, Frankfurt, München
Airlines from your Country:
2. Take Taxi (or Bus) 6km to Skiathos harbor
Tipp: Share Taxi with People an don't pay more than 8 €
3. From Skiathos harbor take the Ferry to Skopelos
Tipp: Here you can book online. When you have time you can also buy your ticket in the office in the harbor. You can choose between, Flying Dolphin, Flying Cat or Big Ferry.
The ticket offices looks (for example) like this: